Basu, D

Bhattacharyya, D P

Biva, Choudhury

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Indian J. Pht/s. 52A, 186-188 (1078)Spectral shape of sea level muons derived from the model of Bull et at using ISR results on kaon-pion ratioD. P. B h a t t a c iia r y y a , B iv a  Ch o u d iiu r y  a n d  D. B asttIndian Aasociaiion for the Cultivation of Science, Jadavpur,Calcutta 700032.{Received 13 May 1977)The piou production spectrum dcuived by different authors from the sea level muon spectrum has been fairly reviewed in our earlier works (Bhattacharj^a 1972j 1974). In these calculations the contribution of kaons in the muon flux was neglected. The Intersecting Storage .Ring experiments of CERN Group (Antinucci el al 1973) have found that the production of kaons in pp collision is not negligible. The average charged piori and kaon multiplicities produced in a pp collision obey the following relations< n „ ± >  ^  1.7Uns+3.7,9-‘*-6_4.3 < n k ± >  == 0.24 In( 1)(2)M^ hero .S' IB ilio square of the total center of mass oiiei-gy. The kaon-pion ratio, <n/c^>  calculated from relations (1) and (2) has been jilotted in thefigure 1 as a function of the square of center of ma.ss energy It is found that the increase of KjTT ratio is very slow.Recently Thompson & Whnlley (1975) have studied the data of Ayre et al (1975) on 2 x particles above 20 GeV muon energy which have provided impetus to ns to consider Rjir ratio from the ISR data lor the production of muons due to decay of kaons as well as pions. We have fitted the ISR data on the K/n ratio in the converntional diffusion model of Bull et al (1965) and have calculated the spectral shape of the sea level muons in the energy range 5-650 GeV.Theoretical model after Bull et al (1965)The diffuHion equation for pious in the atmosphere has been studied by Bull ft al (1965) For (*qual absorption length of protons and interaction length of pious the sea level muon Hpcctruni can be calculated from the following ex­pressionV -IR" tTi v ( W ,  =  4 .p „ (£ „ + A E „ ) - .  {R/c dE^ (3)186spectral shape of sea level mwms 187where the energ,y degradation faetoiB are j„ =  0 757, r* — 0.52; the critical energies for piou and kaon decays are =  121 GeV, Bj. — 450 GeV; is the muon energy loss from production to ground level and is taken from the fol­lowing relation=  2.333GeV+0.0026^;^ ... (4)The muon survival probability is calculated from the expression^  L0.097£;^j(2.33+1.0026^JP'««/t2.«s3+i-«'»3 (5 )and the kaon-pion ratio at production has been taken from the figure 1. It isFig, I, Kaon pion ratio ostimatod from tho CBKN IntereHting Storage Ring data has been plotted as a function of the aqiiuro of total oentor of mass energy,assumed that the exponent of tlic pion and kaon spectra are similar to that of the measured primary proton spectrum of Ryan ei al (1972) which is y — 2.75.The^  calculated sea level ninon spectrum has been fitted to the measured data of Allkofor et al (1971) and Ayro et al (197.5) in the spectral range 5-fi60 GcV. Figure 2 shows the derived sea level muon spectrum with the fitting parameters A — 0.202 and y ~  2.75 along with the experimental data of Kiel and Durham Groups. The theoretical results and experimental data of Allkofor et al(1971) and Ayro et al (1975) have been used in abest values of y  and A. The analysis show that for A =  0.202 and y =  2.75 the calculated spectrum is in accord with the measured values188 D. P. Bhattaoharyya, Biva Ghoudhury and D. BasuThe value for 26 degrees of freedom has been calculated and was found to be 16,63 which corresponds to significance levels of 0.88 for the muon energy range 6-650 GeV,The present study indicates that a single energy exponent (y =  2.75) can explain the entire spectral shape of the energy spectrum of muons derived from the diffusion model of Bull atR bfbrenobbAhkofor 0 . C.. CarstcMen K, & Dau W. D. 1971 PIm. I M .m ,  426.Antinuco. M., Bertin A., Csphuppi P.. D. Agostmo Bruno M-, «molU G. & BuBBiere A. 1973 LeU. Nuovo Gim. 6, 121.Ayro 0. A., Baxendale T. M.. Hume C. J.. Hand. B. 0..Bhattaoharyya D. P. 1972 ZaH.f. Phya. 234, 17.Bhattaoharyya D. P. 1974 J. P% ». A7, 1222.Bob E. M., Nash W. F. & Eastin B. C. 1966 H«o»o Cm. 40. 366.Eyan M. J., Ormoe J. F. & Balasubrahmanyan V. K. 1972 Phya. Bev. Lett.  ^ ,Thompson M. G, & Whalley M. E- 1976 J. Phya. G l, L48,

Spectral Shape of Sea Level Muons Derived from the Model of Bull et al Using ISR Results on Kaon-Pion Ratio

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Spectral Shape of Sea Level Muons Derived from the Model of Bull et al Using ISR Results on Kaon-Pion Ratio

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